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Fractal Frequently Asked Questions and Answers
Section - Chaos

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Q3: What is chaos?  
A3: Chaos is apparently unpredictable behavior arising in a deterministic  
system because of great sensitivity to initial conditions. Chaos arises in a  
dynamical system if two arbitrarily close starting points diverge exponential-  
ly, so that their future behavior is eventually unpredictable.  
  
Weather is considered chaotic since arbitrarily small variations in initial  
conditions can result in radically different weather later. This may limit  
the possibilities of long-term weather forecasting. (The canonical example  
is the possibility of a butterfly's sneeze affecting the weather enough to  
cause a hurricane weeks later.)  
  
Devaney defines a function as chaotic if it has sensitive dependence on ini-  
tial conditions, it is topologically transitive, and periodic points are  
dense. In other words, it is unpredictable, indecomposable, and yet contains  
regularity.  
  
Allgood and Yorke define chaos as a trajectory that is exponentially unstable  
and neither periodic or asymptotically periodic. That is, it oscillates ir-  
regularly without settling down.  
  
The following resources may be helpful to understand chaos:  
  
http://millbrook.lib.rmit.edu.au/exploring.html Exploring Chaos and Fractals  
  
http://www.cc.duth.gr/~mboudour/nonlin.html Chaos and Complexity  
Homepage (M. Bourdour)  
  
gopher://life.anu.edu.au:70/I9/.WWW/complex_systems/lorenz.gif  
Lorenz attractor  
  
http://ucmp1.berkeley.edu/henon.html Experimental interactive  
henon attractor   
  

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Last Update March 27 2014 @ 02:11 PM